He had scarcely arrived in Paspels when a message reached him, requesting a short composition to celebrate Heinrich Strobel's tenth anniversary of service at the Südwestrundfunk, Baden-Baden.

[3] The humorous, caprice-like song—for alto voice, flute, clarinet in A, and bassoon—sets an epigrammatic text written by Strobel, in a French translation by Antoine Goléa.

[6] Upon returning to Cologne, Stockhausen resumed work on Gesang der Jünglinge and returned also to Zeitmaße—now scored for flute, oboe, cor anglais, clarinet, and bassoon—completing a first version that was recorded for the radio in December 1955 by the Wind Quintet of the WDR Symphony Orchestra (led by their oboist, Wilhelm Meyer), and first broadcast in January 1956.

[5] The planned premiere by the WDR Quintet at the Darmstädter Ferienkurse in July 1956 fell through, but Stockhausen brought the score there anyway and showed it to his friends.

Pierre Boulez initially dismissed Zeitmaße with a characteristically cutting remark to the effect that Stockhausen would do better to stay in the electronic studio, but soon changed his mind and asked to programme it in Paris in his Domaine Musical concert series.

[7][8] Five months later, Boulez included Zeitmaße in a programme taken on tour to London—a performance which was broadcast by the BBC on 6 May 1957—and after returning to Paris, made the first recording for commercial release.

[9][10][11] In the meantime, the WDR Quintet had made a recording for broadcast, and in February 1957 gave the German premiere in Bonn, followed in March by a tour to Baden-Baden, Linz, Vienna, and Venice, performing the piece twice on each programme.

In a letter to Wolfgang Steinecke, director of the Darmstadt Courses, Stockhausen reported a "quite unexpectedly huge, genuine success" on every occasion, and that he was "especially surprised by the spontaneous reaction of the Italians".

The other was on that year's announced topic, "Music and Speech", and discussed Boulez's Le Marteau sans maître and Nono's Il canto sospeso, as well as Stockhausen's own Gesang der Jünglinge.

However, because the resulting "fundamental durations" are not small enough for use in the musical detail, subdivisions corresponding to the transposition of the overtones of a pitch's harmonic spectrum are used.

[22] The placement of the instruments on the platform as prescribed in the original version of the score [23] is slightly unconventional (from left to right: oboe, flute, cor anglais, clarinet, bassoon), and is intended to evenly distribute the edgy timbres of the three double-reed instruments across the stage, and balance them with the purer flute and smoother clarinet timbres.

[24] In the revised edition, printed in 1997 and 2004, the order of the instruments on the platform is reversed to read: bassoon, clarinet, cor anglais, flute, oboe.

[27] Durations are governed here by sets of five values, arrayed in a basic square: The first series uses the quaver as counting unit, the next uses semiquavers, and so on.

However, the fifth and twelfth elements (E = 66 and G = 80, respectively) are exchanged, probably because the fourth, fifth, and sixth tempos otherwise would have been too close together:[37] The five cadenzas, which account for about two-fifths of the total duration of Zeitmaße, are spliced into the score in such a way as to flow out of and back into the previously composed music, and yet create a perceivable structure of mutual interruption.